{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T23:35:08Z","timestamp":1649201708832},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,3]]},"abstract":" The problem of making a stable discrete time system chaotic has attracted considerable interest. The definition of chaotification used in these studies is based on introducing a feedback control which establishes the existence of a scrambled set for the controlled system. In this note, we introduce a stronger and potentially more useful definition of chaotification based on the existence of an absolutely continuous invariant measure (acim). The utility of this approach is that once a desired chaotic behavior (in the form of an acim near a stable fixed point) is specified, we can determine a small feedback control (as a function of the stable system) such that the controlled dynamical system exhibits the desired behavior. An example is worked out in detail. <\/jats:p>","DOI":"10.1142\/s0218127406015088","type":"journal-article","created":{"date-parts":[[2006,5,23]],"date-time":"2006-05-23T11:19:24Z","timestamp":1148383164000},"page":"715-719","source":"Crossref","is-referenced-by-count":0,"title":["STRONG CHAOTIFICATION OF DISCRETE TIME SYSTEMS BY SMALL FEEDBACK CONTROL"],"prefix":"10.1142","volume":"16","author":[{"given":"ABRAHAM","family":"BOYARSKY","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada"}]},{"given":"PAWE\u0141","family":"G\u00d3RA","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2024-4"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749600076X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/81.557372"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001236"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764946"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(88)90148-4"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(92)90035-G"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1973-0335758-1"},{"key":"rf9","first-page":"481","volume":"82","author":"Li T. Y.","journal-title":"American Math. Monthly"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(78)90115-4"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499000985"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1109\/81.841926"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-007X(200005\/06)28:3<305::AID-CTA106>3.0.CO;2-P"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403008661"},{"key":"rf15","first-page":"279","volume":"15","author":"Zheng Y.","journal-title":"Int. J. Bifurcation and Chaos"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127406015088","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:10:17Z","timestamp":1565136617000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127406015088"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":15,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1142\/S0218127406015088"],"URL":"https:\/\/doi.org\/10.1142\/s0218127406015088","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}